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Q.

[[1]] is the equation of the parabola whose vertex is O(0,0) and focus is at (−4,0).also find equation of directrix . Find the equation of the parabola with vertex at origin and y+3=0 as its directrix. Also find the focus.


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Detailed Solution

Given.
Vertex = (0,0)
Focus = (−4,0)
seoWe know that Equation parabola y2=-4x
Where ‘a’ = distance from focus to the origin.
= −a=−4 negative distance from origin(−a)
= a=4
= y2=−4×(+4)x
= y2=−16x
Required equation of parabola with vertex (0,0) focus (−4,0)
Now, vertex = (0,0)
Directrix = y+3=0
y=−3
Therefore, directrix  (0,−3)
seo= −a=−3   [∵−a]=negative distance from origin
a=3
Equation of parabola  X2=4ay
X2=4×3×y
X2=12y
 
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